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A267245 T(n,k)=Number of nXk binary arrays with row sums nondecreasing and columns lexicographically nondecreasing. 12
2, 3, 3, 4, 7, 4, 5, 13, 15, 5, 6, 22, 42, 31, 6, 7, 34, 105, 141, 63, 7, 8, 50, 232, 567, 486, 127, 8, 9, 70, 475, 1986, 3351, 1685, 255, 9, 10, 95, 904, 6292, 20040, 20676, 5804, 511, 10, 11, 125, 1632, 18205, 107015, 220235, 129129, 19769, 1023, 11, 12, 161, 2806 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
..2....3......4........5..........6............7..............8
..3....7.....13.......22.........34...........50.............70
..4...15.....42......105........232..........475............904
..5...31....141......567.......1986.........6292..........18205
..6...63....486.....3351......20040.......107015.........516084
..7..127...1685....20676.....220235......2093467.......17892539
..8..255...5804...129129....2499080.....43555569......683027146
..9..511..19769...804817...28501471....924051709....27044976947
.10.1023..66544..4982759..323067002..19614050515..1079112886476
.11.2047.221581.30629206.3626695952.413556580944.42860145907558
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2)
k=3: a(n) = 10*a(n-1) -39*a(n-2) +76*a(n-3) -79*a(n-4) +42*a(n-5) -9*a(n-6)
k=4: [order 10]
k=5: [order 14]
k=6: [order 22]
k=7: [order 32]
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2)
n=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)
n=3: [order 13]
EXAMPLE
Some solutions for n=4 k=4
..0..0..1..1....0..0..0..1....0..0..1..1....0..0..1..1....0..0..1..1
..0..1..1..1....0..1..1..0....0..1..0..1....1..1..0..0....1..1..0..0
..1..0..1..1....0..0..1..1....1..1..0..0....1..1..0..1....1..1..0..0
..1..1..0..1....1..0..1..0....1..1..0..0....1..1..1..0....1..1..0..0
CROSSREFS
Column 1 and row 1 are A000027(n+1).
Column 2 is A000225(n+1).
Row 2 is A002623.
Row 3 is A233302(n-1).
Row 4 is A233303(n-1).
Sequence in context: A241956 A227125 A248944 * A266428 A180985 A227385
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 12 2016
STATUS
approved

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Last modified May 23 22:02 EDT 2024. Contains 372765 sequences. (Running on oeis4.)